MediumMathematicsHigh School (9–10)GeneralTrigonometry › Heights and DistancesNumericalword problemSAT
A building 45 m tall stands back from a river…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A building m tall stands back from a river. From its top, the angle of depression of the near edge of the river is and of the far edge is . Find the width of the river.
Need a reminder? The key ideaShow
For an object at a fixed height , the horizontal distance at each sighting is . The distance moved is the difference of the two distances, and speed is the distance moved divided by the time. A width is a difference of two distances along one line.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The near edge. m from the foot.
Step 2. The far edge. m from the foot.
Step 3. The width. m.
Answer: the river is m wide; its far edge is m from the building.
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